(532g) Large-Area Alignment and Realignment of Cylinder-Forming Block Copolymer Thin Films Via Shear

Introduction

            Thin films of microphase-separated block copolymers are of interest because they form periodic structures on the order of tens of nanometers, with the domain size tunable by molecular weight [1,2] .  Unfortunately, the structures of the as-spun or thermally annealed films do not have the order (neither orientational nor translational) necessary for many intended applications, such as nanowire-grid polarizers templated by cylinder-forming block copolymers [3,4] .  Our group has demonstrated that these block copolymer thin films respond to a shearing field and orient the cylinders in the direction of the imposed stress [5,6] .  This is sufficient if one wants all cylinders to point in a single direction.  For the creation of more complex patterns, the ability of the nanodomains within the film to reorient must be understood. 

            For block copolymer films, no alignment occurs at low shear stresses.  Once the stress reaches a threshold (σ_thresh), the alignment increases quickly as stress increases, and then reaches a plateau where the alignment quality is no longer dependent on stress.  Our group proposed a phenomenological model to explain the shear alignment process [6,7].  The model posits that there is an effective order-disorder transition temperature (T_ODT*) that is a function of the misalignment a grain has with the shear direction (dθ):  T_ODT* = T_ODT(1-(σ/σ_c)²sin²(dθ)).  Here, σ is the applied stress and σ_c is the critical stress, which is given by σ_thresh = σ_c(1-T/T_ODT)^1/2.  The rate of melting/recrystallization of a grain is assumed constant:  dR/dt = Γ(T_ODT*-T)/T_ODT with R as the area of a grain and Γ as a rate constant that determines how quickly the alignment plateau is reached.  This model has two empirical parameters:  σ_c and Γ.  Fitting experimental data taken at different temperatures for cylinder-forming block copolymers showed excellent agreement with the model [6].  These tests were made on films sheared from the isotropic state, with an ensemble of grains in all orientations.  Here, we directly test the model's idea that ?melting? is dependent on σ and dθ by varying them in a continuous and known way through shearing the ordered film a second time, in a different direction, with the aim of reorienting the cylindrical microdomains.

Experimental

            The diblock copolymer used in this study, PS-PEP 5/13 (5 kg/mol polystyrene  and 13 kg/mol poly(ethylene-alt-propylene)), has been characterized previously [8] with a bulk T_ODT = 481 K and an intercylinder spacing of 20 nm.  Dilute solutions (1-2 % in toluene) were spin-coated onto bare halves of 3? silicon wafers from Silicon Quest International to obtain a monolayer of cylinders (27 nm).  The wafers were then secured to the Peltier heater on an Anton Paar MCR 501 constant stress rheometer.  A thick layer (~0.2 mm) of polydimethylsiloxane (PDMS) oil (1E6 cSt from Gelest) was placed on top of the thin film before the parallel plate rheometer tool was lowered into place.  The film was sheared at a constant temperature and rotation rate for a set amount of time.  The wafer and film were then translated relative to the rotation axis, reattached to the heater, the oil reapplied, and the film sheared a second time.  The overlap region between the two shears is the area of interest, where we have continuous gradients in both stress (σ) and misalignment angle (dθ). Following shearing, the oil was removed by absorption into a crosslinked PDMS pad.  Both real-space images (of the PS cylinders) and moiré interference patterns are captured with a Dimension 3000 atomic force microscope in Tapping Mode.  Custom software is used to filter the real-space images and quantify the alignment by calculating an orientational order parameter, ψ₂ = < cos(2dθ) >.  The angular distribution, A(dθ), of the film can be determined from the Fourier transform of the moiré pattern [9].  The order parameter can then be calculated as:

           
                                                                               (1)

Results and Discussion

            Real-space images of the film following the first shear showed that alignment can be achieved at high stresses (> 600 Pa).  At low stresses no alignment was observed ? only grains of all orientations.  In fact, it was difficult to detect the transition region previously seen for sphere-forming [7,10] or other cylinder-forming block copolymers [6].  The transition region is thought to be hidden behind the large amount of scatter present in the low stress-data ? a consequence of the imaging window being smaller than the correlation length of the block copolymer cylinders [8].  Attempts were made to fit the melting/recrystallization model to the results from the single-shear experiments.  A narrow transition region indicates that the melting/recrystallization process is saturated with time (longer shearing will not lead to better ordering), which limits what can be said about the rate constant:  Γ > 0.1 sec^-1.  A Levenberg-Marquardt algorithm was used to fit the model to the experimental data to determine the critical stress:  σ_c = 600±400
Pa.  The large uncertainty is caused by the scatter near σ_thresh.

            Moiré pattern imaging was used to reduce the scatter in the low-stress region, since using the interference pattern increases the image window size by an order of magnitude, to the same size as the correlation length.  Results showed a sharp transition at 500?600 Pa, which still limits Γ to be greater than 0.1 sec^-1, but an accurate determination of σ_c is now possible:  σ_c = 900±100 Pa.  It appears that PS-PEP 5/13 does indeed obey the melting/recrystallization model.  One can view the angular distribution to see that below 500 Pa, grains of all orientations are present.  In the transition region, the grains at the greatest mismatch to the shear direction are destroyed and a Gaussian-like distribution centered at dθ = 0 forms which narrows with increasing stress. 

            Double shearing was used to test the model's idea that ?melting? depends on both stress (σ) and misalignment angle (dθ).  The overlap region of the two shearing circles is the area of interest and principally contains aligned grains of an orientation which is ideally given by the melting/recrystallization model.  Of particular interest is the contour line at dθ = 90°, where complete reorientation will need to take place: in other words, the second shear reorients the cylinders to be perpendicular to their original direction.  Since we are interested in reorientation of grains, real-space images were sufficient because images below σ_thresh would still be aligned with the first shear direction, clearly revealing the value of σ_thresh.  The results of the double-shear experiment do agree very well with the melting/recrystallization model, with the transition from alignment in one direction to alignment in the new shearing direction occurring at the predicted stress.  This contrasts with previous work on double shearing of sphere-forming block copolymers [11], which showed that a larger stress is required to realign the thin film (σ_c increased by a factor of 2.5) relative to the stress required to generate alignment from an initially polygrain state.  For PS-PEP 5/13, refitting the model to the double-shear data yielded parameters that are consistent with those derived by shearing from the polygrain state:  Γ > 0.1 sec^-1 and σ_c = 1000±100
Pa.

            We also observed grain boundary generation within the region transitioning between alignment with the first shear to alignment with the second shear.  This is expected within the context of the melting/recrystallization model where sections of the film must ?melt? and then ?recrystallize? in the preferred orientation dictated by the shearing field.  This melting/recrystalliztion can occur along a front resulting in the observed grain boundaries.  In summary, our model represents the shear-alignment process well by quantitatively capturing the transitions for both alignment and realignment of cylinder-forming block copolymer thin films, and provides the basis for the design of processes whereby tailored local orientation of the cylindrical microdomains can be achieved [6].

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